CAREER: Demystifying Deep Machine Learning Models using Convex Optimization for Reliable AI

该项目为深度神经网络开发了一个理论框架，深度神经网络是一种机器学习模型，在图像和语音识别、机器人和自动化等一系列应用中取得了巨大成功。尽管这些模型取得了成功，但在理解它们如何做出决策或如何使它们更有效，更强大和更可靠方面仍然存在重大的开放问题。此外，深度神经网络的内部工作缺乏透明度，这可能使人们难以信任它们的输出并解释它们的结果。通过开发一个理论框架来研究和训练这些基于凸性的模型，凸性是优化理论中一个研究得很好的数学概念，该项目旨在提高其可靠性和可解释性，最终导致更有效和更值得信赖的人工智能系统。该项目还旨在培养下一代研究人员，并通过安全有效地应用人工智能来造福社会。该技术方法基于一种新颖的凸分析框架，用于研究，训练和验证非凸模型，包括深度神经网络。通过利用非凸训练损失中隐藏的凸优化景观，该项目开发了一个理论基础，可以揭开这些模型的优化和泛化特性的神秘面纱。通过应用信号处理，压缩感知和凸优化技术，该项目旨在统一来自不同领域的思想和方法，以推进非凸模型的最新技术。这将促进我们对深度神经网络基本行为的理解，并减轻与其使用相关的挑战。此外，本计画将透过凸最佳化的透镜，探讨这些模型在实际应用中的可解释性、可验证性与稳健性。神经网络的多样化应用可以吸引不同背景的研究生，并有助于将现代深度学习主题融入信号处理课程。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

This project develops a theoretical framework for deep neural networks, a type of machine learning model that has had tremendous success in a range of applications including image and speech recognition, robotics, and automation. Although these models have been successful, there remain significant open questions in the understanding of how they make decisions or how they can be made more efficient, robust and reliable. Additionally, there is a lack of transparency in the inner workings of deep neural networks, which can make it difficult to trust their output and interpret their results. By developing a theoretical framework to study and train these models based on convexity, which is a well-studied mathematical concept in optimization theory, this project aims to improve their reliability and interpretability, ultimately leading to more efficient and trustworthy artificial intelligence systems. This project likewise seeks to educate the next generation of researchers, and benefit society by enabling safe and effective applications of artificial intelligence.The technical approach is based on a novel convex analytic framework to study, train, and validate non-convex models, including deep neural networks. By leveraging the hidden convex optimization landscape in non-convex training losses, this project develops a theoretical foundation that should demystify the optimization and generalization properties of these models. By applying techniques from signal processing, compressed sensing and convex optimization, the project seeks to unify ideas and methods from diverse fields in order to advance the state of the art in non-convex models. This will advance our understanding of the fundamental behavior of deep neural networks and mitigate challenges associated with their use. In addition, this project will investigate the interpretability, verifiability and robustness of these models through the lens of convex optimization in practical applications. The diverse applications of neural networks can attract graduate students with diverse backgrounds and contribute to the integration of modern deep learning topics in signal processing courses.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.